Question: Reduce to lowest terms: $ \dfrac{5}{3} \div - \dfrac{2}{3} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{2}{3}$ is $- \dfrac{3}{2}$ Therefore: $ \dfrac{5}{3} \div - \dfrac{2}{3} = \dfrac{5}{3} \times - \dfrac{3}{2} $ $ \phantom{ \dfrac{5}{3} \times - \dfrac{3}{2}} = \dfrac{5 \times -3}{3 \times 2} $ $ \phantom{ \dfrac{5}{3} \times - \dfrac{3}{2}} = \dfrac{-15}{6} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{-15}{6} = \dfrac{-15 \div 3}{6 \div 3} = -\dfrac{5}{2} $